1. **Triangle problem:** Given a right triangle with base segments 7.3 cm and 2.7 cm, the vertical side opposite angle $\theta$ is $7.3 - 2.7 = 4.6$ cm, and the total base is $7.3 + 2.7 = 10.0$ cm. 2. To find the hypotenuse $k$, use the Pythagorean theorem: $$k = \sqrt{(10.0)^2 + (4.6)^2} = \sqrt{100 + 21.16} = \sqrt{121.16} \approx 11.0 \text{ cm}$$ 3. To find $\cos \theta$, use the adjacent side over hypotenuse: $$\cos \theta = \frac{10.0}{11.0} \approx 0.909$$ --- 4. **Distance between points A(3,23) and B(15,48):** Use the distance formula: $$d = \sqrt{(15 - 3)^2 + (48 - 23)^2} = \sqrt{12^2 + 25^2} = \sqrt{144 + 625} = \sqrt{769} \approx 27.7$$ --- 5. **Angle $\theta$ between lines $y=3x+4$ and $y=4$:** The horizontal line $y=4$ has slope $m_1=0$. The line $y=3x+4$ has slope $m_2=3$. The angle between two lines with slopes $m_1$ and $m_2$ is: $$\tan \theta = \left| \frac{m_2 - m_1}{1 + m_1 m_2} \right| = \left| \frac{3 - 0}{1 + 0} \right| = 3$$ So, $$\theta = \arctan(3) \approx 71.6^\circ \approx 72^\circ$$ --- 6. **Number cards median and range problem:** Median is 6, range is 14, and cards are 1, 5, ?, ?. 7. **Mean of three cards is 5:** Cards are 4, 9, and ?. Mean formula: $$\frac{4 + 9 + x}{3} = 5 \implies 13 + x = 15 \implies x = 2$$ 8. **Total of all three cards:** $$4 + 9 + 2 = 15$$ --- **Final answers:** - Hypotenuse $k \approx 11.0$ cm - $\cos \theta \approx 0.909$ - Distance between A and B $\approx 27.7$ - Angle $\theta \approx 72^\circ$ - Missing number replacing question mark in last card is $2$ - Total of three cards is $15$